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Fischer matrices of Dempwolff group 25GL(5,2) | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 1، شماره 4، اسفند 2012، صفحه 43-63 اصل مقاله (622.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2012.1590 | ||
| نویسندگان | ||
| Ayoub Basheer Mohammed Basheer* 1؛ Jamshid Moori2 | ||
| 1Universities of KwaZulu-Natal and Khartoum | ||
| 2North-West University | ||
| چکیده | ||
| In [U. Dempwolff, On extensions of elementary abelian groups of order $2^{5}$ by $GL(5,2)$, Rend. Sem. Mat. Univ. Padova, 48 (1972) 359 - 364.] Dempwolff proved the existence of a group of the form $2^{5}{^{\cdot}}GL(5,2)$ (a non split extension of the elementary abelian group $2^{5}$ by the general linear group $GL(5,2)$). This group is the second largest maximal subgroup of the sporadic Thompson simple group $\mathrm{Th}.$ In this paper we calculate the Fischer matrices of Dempwolff group $\overline{G} = 2^{5}{^{\cdot}}GL(5,2).$ The theory of projective characters is involved and we have computed the Schur multiplier together with a projective character table of an inertia factor group. The full character table of $\overline{G}$ is then can be calculated easily. | ||
| کلیدواژه‌ها | ||
| Group extensions؛ Dempwolff group؛ character table؛ Clifford Theory؛ inertia groups؛ Fischer matrices؛ Schur multiplier؛ projective characters؛ covering group | ||
| مراجع | ||
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